We propose a deep learning method to build an AdS/QCD model from the data of hadron spectra. A major problem of generic AdS/QCD models is that a large ambiguity is allowed for the bulk gravity metric with which QCD observables are holographically calculated. We adopt the experimentally measured spectra of ρ and a 2 mesons as training data, and perform a supervised machine learning which determines concretely a bulk metric and a dilaton profile of an AdS/QCD model. Our deep learning (DL) architecture is based on the AdS/DL correspondence [K. Hashimoto, S. Sugishita, A. Tanaka, and A. Tomiya, Phys. Rev. D 98, 046019 (2018)] where the deep neural network is identified with the emergent bulk spacetime.
We derive an explicit form of the dilaton potential in improved holographic QCD (IHQCD) from the QCD lattice data of the chiral condensate as a function of the quark mass. This establishes a data-driven holographic modeling of QCD -machine learning holographic QCD. The modeling consists of two steps for solving inverse problems. The first inverse problem is to find the emergent bulk geometry consistent with the lattice QCD simulation data at the boundary. We solve this problem with the refinement of neural ordinary differential equation, a machine learning technique. The second inverse problem is to derive a bulk gravity action with a dilaton potential such that its solution is the emergent bulk geometry. We solve this problem at non-zero temperature, and derive the explicit form of the dilaton potential. The dilaton potential determines the bulk action, the Einstein-dilaton system, thus we derive holographically the bulk system from the QCD chiral condensate data. The usefulness of the model is shown in the example of the prediction of the string breaking distance, whose value is found to be consistent with another lattice QCD data.
We derive an explicit form of the dilaton potential in improved holographic QCD (IHQCD) from the QCD lattice data of the chiral condensate as a function of the quark mass. This establishes a data-driven holographic modeling of QCD — machine learning holographic QCD. The modeling consists of two steps for solving inverse problems. The first inverse problem is to find the emergent bulk geometry consistent with the lattice QCD simulation data at the boundary. We solve this problem with the refinement of neural ordinary differential equation, a machine learning technique. The second inverse problem is to derive a bulk gravity action with a dilaton potential such that its solution is the emergent bulk geometry. We solve this problem at non-zero temperature, and derive the explicit form of the dilaton potential. The dilaton potential determines the bulk action, the Einstein-dilaton system, thus we derive holographically the bulk system from the QCD chiral condensate data. The usefulness of the model is shown in the example of the prediction of the string breaking distance, whose value is found to be consistent with another lattice QCD data.
We study 1/N corrections to a Wilson loop in holographic duality. Extending the AdS/CFT correspondence beyond the large N limit is an important but a subtle issue, as it needs quantum gravity corrections in the gravity side. To find a physical property of the quantum corrected geometry of near-horizon black 0-branes previously obtained by Hyakutake, we evaluate a Euclidean string worldsheet hanging down in the geometry, which corresponds to a rectangular Wilson loop in the SU (N ) quantum mechanics with 16 supercharges at a finite temperature with finite N . We find that the potential energy defined by the Wilson loop increases due to the 1/N correction, therefore the quantum gravity correction weakens the gravitational attraction.2 The repulsive wall structure was also found in a probe D0-brane potential in the quantum corrected geometry [6].3 Since we treat D0-branes, there is only one direction in their worldvolume: time. To form a rectangular Wilson loop, the other direction is necessary, and here we take it to be a direction in S 8 which is spanned by the scalar field of the quantum mechanics. Therefore the two separated D0-branes are located in different positions. This kind of situation was treated originally in Ref. [13]. 4 See also Refs. [15,16] for the history of the matching in the AdS/CFT. For circular Wilson loops with a totally symmetric/antisymmetric representation of SU (N ) whose dual is not a string but a D3-brane/D5brane, see Refs. [17,18].-2 -
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